Unsupervised Learning: Trade & Ahead

Problem Statement

Context

The stock market has consistently proven to be a good place to invest in and save for the future. There are a lot of compelling reasons to invest in stocks. It can help in fighting inflation, create wealth, and also provides some tax benefits. Good steady returns on investments over a long period of time can also grow a lot more than seems possible. Also, thanks to the power of compound interest, the earlier one starts investing, the larger the corpus one can have for retirement. Overall, investing in stocks can help meet life's financial aspirations.

It is important to maintain a diversified portfolio when investing in stocks in order to maximise earnings under any market condition. Having a diversified portfolio tends to yield higher returns and face lower risk by tempering potential losses when the market is down. It is often easy to get lost in a sea of financial metrics to analyze while determining the worth of a stock, and doing the same for a multitude of stocks to identify the right picks for an individual can be a tedious task. By doing a cluster analysis, one can identify stocks that exhibit similar characteristics and ones which exhibit minimum correlation. This will help investors better analyze stocks across different market segments and help protect against risks that could make the portfolio vulnerable to losses.

Objective

Trade&Ahead is a financial consultancy firm who provide their customers with personalized investment strategies. They have hired you as a Data Scientist and provided you with data comprising stock price and some financial indicators for a few companies listed under the New York Stock Exchange. They have assigned you the tasks of analyzing the data, grouping the stocks based on the attributes provided, and sharing insights about the characteristics of each group.

Data Dictionary

• Ticker Symbol: An abbreviation used to uniquely identify publicly traded shares of a particular stock on a particular stock market
• Company: Name of the company
• GICS Sector: The specific economic sector assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• GICS Sub Industry: The specific sub-industry group assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• Current Price: Current stock price in dollars
• Price Change: Percentage change in the stock price in 13 weeks
• Volatility: Standard deviation of the stock price over the past 13 weeks
• ROE: A measure of financial performance calculated by dividing net income by shareholders' equity (shareholders' equity is equal to a company's assets minus its debt)
• Cash Ratio: The ratio of a company's total reserves of cash and cash equivalents to its total current liabilities
• Net Cash Flow: The difference between a company's cash inflows and outflows (in dollars)
• Net Income: Revenues minus expenses, interest, and taxes (in dollars)
• Earnings Per Share: Company's net profit divided by the number of common shares it has outstanding (in dollars)
• Estimated Shares Outstanding: Company's stock currently held by all its shareholders
• P/E Ratio: Ratio of the company's current stock price to the earnings per share
• P/B Ratio: Ratio of the company's stock price per share by its book value per share (book value of a company is the net difference between that company's total assets and total liabilities)

Importing necessary libraries

# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

sns.set_theme(style='darkgrid')

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

# to scale the data using z-score
from sklearn.preprocessing import StandardScaler
from scipy.stats import zscore

# to compute distances
from scipy.spatial.distance import cdist, pdist

# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet

# to suppress warnings
import warnings
warnings.filterwarnings("ignore")

Loading the dataset

# mount Google Drive to upload data from the drive
from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive

# download, read & assign data to a variable
pd.read_csv('/content/drive/MyDrive/DataSets/stock_data.csv')
stock_data = pd.read_csv('/content/drive/MyDrive/DataSets/stock_data.csv')

Overview of the Dataset

Checking the shape of the dataset

#checking the shape of the data
stock_data.shape

(340, 15)

#checking the shape of the data
stock_data.shape
print(f"There are {stock_data.shape[0]} rows and {stock_data.shape[1]} columns.")

There are 340 rows and 15 columns.

Displaying few rows of the dataset

# view the first 5 rows of the train datasets
stock_data.head()

	Ticker Symbol	Security	GICS Sector	GICS Sub Industry	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio
0	AAL	American Airlines Group	Industrials	Airlines	42.349998	9.999995	1.687151	135	51	-604000000	7610000000	11.39	6.681299e+08	3.718174	-8.784219
1	ABBV	AbbVie	Health Care	Pharmaceuticals	59.240002	8.339433	2.197887	130	77	51000000	5144000000	3.15	1.633016e+09	18.806350	-8.750068
2	ABT	Abbott Laboratories	Health Care	Health Care Equipment	44.910000	11.301121	1.273646	21	67	938000000	4423000000	2.94	1.504422e+09	15.275510	-0.394171
3	ADBE	Adobe Systems Inc	Information Technology	Application Software	93.940002	13.977195	1.357679	9	180	-240840000	629551000	1.26	4.996437e+08	74.555557	4.199651
4	ADI	Analog Devices, Inc.	Information Technology	Semiconductors	55.320000	-1.827858	1.701169	14	272	315120000	696878000	0.31	2.247994e+09	178.451613	1.059810

# view a sample of the data
stock_data.sample(n=10, random_state=1)

	Ticker Symbol	Security	GICS Sector	GICS Sub Industry	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio
102	DVN	Devon Energy Corp.	Energy	Oil & Gas Exploration & Production	32.000000	-15.478079	2.923698	205	70	830000000	-14454000000	-35.55	4.065823e+08	93.089287	1.785616
125	FB	Facebook	Information Technology	Internet Software & Services	104.660004	16.224320	1.320606	8	958	592000000	3669000000	1.31	2.800763e+09	79.893133	5.884467
11	AIV	Apartment Investment & Mgmt	Real Estate	REITs	40.029999	7.578608	1.163334	15	47	21818000	248710000	1.52	1.636250e+08	26.335526	-1.269332
248	PG	Procter & Gamble	Consumer Staples	Personal Products	79.410004	10.660538	0.806056	17	129	160383000	636056000	3.28	4.913916e+08	24.070121	-2.256747
238	OXY	Occidental Petroleum	Energy	Oil & Gas Exploration & Production	67.610001	0.865287	1.589520	32	64	-588000000	-7829000000	-10.23	7.652981e+08	93.089287	3.345102
336	YUM	Yum! Brands Inc	Consumer Discretionary	Restaurants	52.516175	-8.698917	1.478877	142	27	159000000	1293000000	2.97	4.353535e+08	17.682214	-3.838260
112	EQT	EQT Corporation	Energy	Oil & Gas Exploration & Production	52.130001	-21.253771	2.364883	2	201	523803000	85171000	0.56	1.520911e+08	93.089287	9.567952
147	HAL	Halliburton Co.	Energy	Oil & Gas Equipment & Services	34.040001	-5.101751	1.966062	4	189	7786000000	-671000000	-0.79	8.493671e+08	93.089287	17.345857
89	DFS	Discover Financial Services	Financials	Consumer Finance	53.619999	3.653584	1.159897	20	99	2288000000	2297000000	5.14	4.468872e+08	10.431906	-0.375934
173	IVZ	Invesco Ltd.	Financials	Asset Management & Custody Banks	33.480000	7.067477	1.580839	12	67	412000000	968100000	2.26	4.283628e+08	14.814159	4.218620

Checking the data types of the columns for the dataset

# checking the column names and datatypes
stock_data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 340 entries, 0 to 339
Data columns (total 15 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   Ticker Symbol                 340 non-null    object 
 1   Security                      340 non-null    object 
 2   GICS Sector                   340 non-null    object 
 3   GICS Sub Industry             340 non-null    object 
 4   Current Price                 340 non-null    float64
 5   Price Change                  340 non-null    float64
 6   Volatility                    340 non-null    float64
 7   ROE                           340 non-null    int64  
 8   Cash Ratio                    340 non-null    int64  
 9   Net Cash Flow                 340 non-null    int64  
 10  Net Income                    340 non-null    int64  
 11  Earnings Per Share            340 non-null    float64
 12  Estimated Shares Outstanding  340 non-null    float64
 13  P/E Ratio                     340 non-null    float64
 14  P/B Ratio                     340 non-null    float64
dtypes: float64(7), int64(4), object(4)
memory usage: 40.0+ KB

Creating a copy of original data

# copying the data to another variable to avoid any changes to original data
stock = stock_data.copy()

Checking for duplicates and missing values

# check for duplicate values
stock.duplicated().sum() 

0

# check for missing values in the data
stock.isnull().sum() 

Ticker Symbol                   0
Security                        0
GICS Sector                     0
GICS Sub Industry               0
Current Price                   0
Price Change                    0
Volatility                      0
ROE                             0
Cash Ratio                      0
Net Cash Flow                   0
Net Income                      0
Earnings Per Share              0
Estimated Shares Outstanding    0
P/E Ratio                       0
P/B Ratio                       0
dtype: int64

Statistical summary of the dataset

stock.describe(include='all').T

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
Ticker Symbol	340	340	AAL	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Security	340	340	American Airlines Group	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN
GICS Sector	340	11	Industrials	53	NaN	NaN	NaN	NaN	NaN	NaN	NaN
GICS Sub Industry	340	104	Oil & Gas Exploration & Production	16	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Current Price	340.0	NaN	NaN	NaN	80.862345	98.055086	4.5	38.555	59.705	92.880001	1274.949951
Price Change	340.0	NaN	NaN	NaN	4.078194	12.006338	-47.129693	-0.939484	4.819505	10.695493	55.051683
Volatility	340.0	NaN	NaN	NaN	1.525976	0.591798	0.733163	1.134878	1.385593	1.695549	4.580042
ROE	340.0	NaN	NaN	NaN	39.597059	96.547538	1.0	9.75	15.0	27.0	917.0
Cash Ratio	340.0	NaN	NaN	NaN	70.023529	90.421331	0.0	18.0	47.0	99.0	958.0
Net Cash Flow	340.0	NaN	NaN	NaN	55537620.588235	1946365312.175789	-11208000000.0	-193906500.0	2098000.0	169810750.0	20764000000.0
Net Income	340.0	NaN	NaN	NaN	1494384602.941176	3940150279.327936	-23528000000.0	352301250.0	707336000.0	1899000000.0	24442000000.0
Earnings Per Share	340.0	NaN	NaN	NaN	2.776662	6.587779	-61.2	1.5575	2.895	4.62	50.09
Estimated Shares Outstanding	340.0	NaN	NaN	NaN	577028337.75403	845849595.417695	27672156.86	158848216.1	309675137.8	573117457.325	6159292035.0
P/E Ratio	340.0	NaN	NaN	NaN	32.612563	44.348731	2.935451	15.044653	20.819876	31.764755	528.039074
P/B Ratio	340.0	NaN	NaN	NaN	-1.718249	13.966912	-76.119077	-4.352056	-1.06717	3.917066	129.064585

Observation

The datasates has 15 features, 4 are of categorical datatypes and the remaining 11 are numerical datatypes.

It also have 340 observations for each feature.

There are no missing nor duplicated information in the dataset.

From the Statistical Summary, most of the distibution are right skewed.

Exploratory Data Analysis

Univariate analysis

Distribution of Stock Price

sns.boxplot(data = stock, x = 'Current Price')
plt.title('Boxplot of Current Price')
plt.xlabel('Current Price')
plt.show();

Distribution of Percentage change in the stock price

sns.boxplot(data = stock, x = 'Price Change')
plt.title('Boxplot of Price Change')
plt.xlabel('Price Change')
plt.show();

Distribution of Volatility

sns.boxplot(data = stock, x = 'Volatility')
plt.title('Boxplot of Volatility')
plt.xlabel('Volatility')
plt.show();

Distribution of ROE

sns.boxplot(data = stock, x = 'ROE')
plt.title('Boxplot of ROE')
plt.xlabel('ROE')
plt.show();

Distribution of Cash Ratio

sns.boxplot(data = stock, x = 'Cash Ratio')
plt.title('Boxplot of Cash Ratio')
plt.xlabel('Cash Ratio')
plt.show();

Distribution of Net Cash Flow

sns.boxplot(data = stock, x = 'Net Cash Flow')
plt.title('Boxplot of Net Cash Flow')
plt.xlabel('Net Cash Flow')
plt.show();

Distribution of Net Income

sns.boxplot(data = stock, x = 'Net Income')
plt.title('Boxplot of Net Income')
plt.xlabel('Net Income')
plt.show();

Distribution of Earnings Per Share

sns.boxplot(data = stock, x = 'Earnings Per Share')
plt.title('Boxplot of Earnings Per Share')
plt.xlabel('Earnings Per Share')
plt.show();

Distribution of Estimated Shares Outstanding

sns.boxplot(data = stock, x = 'Estimated Shares Outstanding')
plt.title('Boxplot of Estimated Shares Outstanding')
plt.xlabel('Estimated Shares Outstanding')
plt.show();

Distribution of P/E Ratio

sns.boxplot(data = stock, x = 'P/E Ratio')
plt.title('Boxplot of P/E Ratio')
plt.xlabel('P/E Ratio')
plt.show();

Distribution of P/B Ratio

sns.boxplot(data = stock, x = 'P/B Ratio')
plt.title('Boxplot of P/B Ratio')
plt.xlabel('P/B Ratio')
plt.show();

Distribution of GICS Sector

sns.countplot(data = stock, x = 'GICS Sector')
plt.title('Distribution of GICS Sector')
plt.xlabel('GICS Sector')
plt.ylabel('Count')
plt.xticks(rotation=90)
plt.show()

Distribution of GICS Sub Industry

plt.figure(figsize=(15, 7))
sns.countplot(data = stock, x = 'GICS Sub Industry')
plt.title('Distribution of GICS Sub Industryr')
plt.xlabel('GICS Sub Industry')
plt.ylabel('Count')
plt.xticks(rotation=90)
plt.show()

Bivariate Analysis

num_col = ['Current Price', 'Price Change', 'Volatility', 'ROE', 'Cash Ratio', 'Net Cash Flow',
           'Net Income', 'Earnings Per Share', 'Estimated Shares Outstanding','P/E Ratio', 'P/B Ratio']

# correlation check
plt.figure(figsize=(15, 7))
sns.heatmap(
    stock.corr(), annot=True, vmin=-1, vmax=1, fmt='.2f', cmap = 'Spectral'
)
plt.show()

scaled_stock = stock.iloc[:,4:].apply(zscore)
sns.pairplot(data = scaled_stock, diag_kind="kde")
plt.show()

Analyzing price increase Distribution Among Different Economic Sectors

plt.figure(figsize=(15,8))
sns.barplot(data = stock, x='Price Change', y='GICS Sector', ci=False) 
plt.xticks(rotation=90)
plt.show()

Analyzing Cash ratios Distribution Among Different Economic Sectors

plt.figure(figsize=(15,8))
sns.barplot(data = stock, x='Cash Ratio', y='GICS Sector', ci=False)  
plt.xticks(rotation=90)
plt.show()

Analyzing P/E ratios Distribution Among Different Economic Sectors

plt.figure(figsize=(15,8))
sns.barplot(data = stock, x='P/E Ratio', y='GICS Sector', ci=False)  
plt.xticks(rotation=90)
plt.show()

Analyzing Volatility Distribution Among Different Economic Sectors

plt.figure(figsize=(15,8))
sns.barplot(data = stock, x='Volatility', y='GICS Sector', ci=False) 
plt.xticks(rotation=90)
plt.show()

Observations

There isn't high correlation between the numerical features.

Energy, Healthcare, Telecommunications Services and Informatio Technology are industries doing well with Cash Ratio, Volatility, price changes and P/E Ratios.

Data Preprocessing

Outlier Check

plot the boxplots for the numerical features to check for outliers.

plt.figure(figsize=(15, 12))

numeric_columns = stock.select_dtypes(include=np.number).columns.tolist()

for i, variable in enumerate(numeric_columns):
    plt.subplot(3, 4, i + 1)
    plt.boxplot(stock[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()

Scaling

scale the data .

# scaling the data before clustering
scaler = StandardScaler()
#subset = stock[num_col].copy() 
subset = stock.iloc[:,4:]
subset_scaled = scaler.fit_transform(subset)

# creating a dataframe of the scaled data
subset_scaled_stock = pd.DataFrame(subset_scaled, columns = subset.columns)

Observations

There are lots of outliers present in the dataset.

K-means Clustering

Checking Elbow Plot

k_means_stock = subset_scaled_stock.copy()

clusters = range(1, 15)
meanDistortions = []

for k in clusters:
    model = KMeans(n_clusters=k, random_state=1)
    model.fit(subset_scaled_stock)
    prediction = model.predict(k_means_stock)
    distortion = (
                sum(np.min(cdist(k_means_stock, model.cluster_centers_, 'euclidean'), axis=1))
        / k_means_stock.shape[0]
    )

    meanDistortions.append(distortion)

    print('Number of Clusters:', k, '\tAverage Distortion:', distortion)

plt.plot(clusters, meanDistortions, 'bx-')
plt.xlabel('k')
plt.ylabel('Average Distortion')
plt.title('Selecting k with the Elbow Method', fontsize=20)
plt.show()

Number of Clusters: 1 	Average Distortion: 2.5425069919221697
Number of Clusters: 2 	Average Distortion: 2.382318498894466
Number of Clusters: 3 	Average Distortion: 2.2692367155390745
Number of Clusters: 4 	Average Distortion: 2.1745559827866363
Number of Clusters: 5 	Average Distortion: 2.128799332840716
Number of Clusters: 6 	Average Distortion: 2.080400099226289
Number of Clusters: 7 	Average Distortion: 2.0289794220177395
Number of Clusters: 8 	Average Distortion: 1.964144163389972
Number of Clusters: 9 	Average Distortion: 1.9221492045198068
Number of Clusters: 10 	Average Distortion: 1.8513913649973124
Number of Clusters: 11 	Average Distortion: 1.8024134734578485
Number of Clusters: 12 	Average Distortion: 1.7900931879652673
Number of Clusters: 13 	Average Distortion: 1.7417609203336912
Number of Clusters: 14 	Average Distortion: 1.673559857259703

model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(1, 15), timings=True)
# fit the data to the visualizer
visualizer.fit(k_means_stock) 
# finalize and render figure
visualizer.show() 

<Axes: title={'center': 'Distortion Score Elbow for KMeans Clustering'}, xlabel='k', ylabel='distortion score'>

check the silhouette scores

sil_score = []
cluster_list = range(2, 15)
for n_clusters in cluster_list:
    clusterer = KMeans(n_clusters = n_clusters, random_state=1)
    preds = clusterer.fit_predict((subset_scaled_stock))
    score = silhouette_score(k_means_stock, preds)
    sil_score.append(score)
    print('For n_clusters = {}, the silhouette score is {})'.format(n_clusters, score))

plt.plot(cluster_list, sil_score)
plt.show()

For n_clusters = 2, the silhouette score is 0.43969639509980457)
For n_clusters = 3, the silhouette score is 0.4644405674779404)
For n_clusters = 4, the silhouette score is 0.4577225970476733)
For n_clusters = 5, the silhouette score is 0.43228336443659804)
For n_clusters = 6, the silhouette score is 0.4005422737213617)
For n_clusters = 7, the silhouette score is 0.3976335364987305)
For n_clusters = 8, the silhouette score is 0.40278401969450467)
For n_clusters = 9, the silhouette score is 0.3778585981433699)
For n_clusters = 10, the silhouette score is 0.13458938329968687)
For n_clusters = 11, the silhouette score is 0.1421832155528444)
For n_clusters = 12, the silhouette score is 0.2044669621527429)
For n_clusters = 13, the silhouette score is 0.23424874810104204)
For n_clusters = 14, the silhouette score is 0.12102526472829901)

13 clusters indicates a high silhouette coefficient, with a values closest to one(1) and at the time having a low variability.

model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(2, 15), metric = 'silhouette', timings=True)
# fit the data to the visualizer
visualizer.fit(k_means_stock)
# finalize and render figure
visualizer.show()

<Axes: title={'center': 'Silhouette Score Elbow for KMeans Clustering'}, xlabel='k', ylabel='silhouette score'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(13, random_state=1))
## Complete the code to visualize the silhouette scores for certain number of clusters
visualizer.fit(k_means_stock)
visualizer.show()

<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 340 Samples in 13 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

Creating Final Model

# final K-means model
kmeans = KMeans(n_clusters = 13 , random_state=1) 
## Complete the code to choose the number of clusters
kmeans.fit(k_means_stock)

KMeans(n_clusters=13, random_state=1)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

# creating a copy of the original data
stock1 = stock.copy()

# adding kmeans cluster labels to the original and scaled dataframes
k_means_stock['KM_segments'] = kmeans.labels_
stock1['KM_segments'] = kmeans.labels_

Cluster Profiling

km_cluster_profile = stock1.groupby('KM_segments').mean() 

km_cluster_profile['count_in_each_segment'] = (
    stock1.groupby('KM_segments')['Security'].count().values  
)

km_cluster_profile.style.highlight_max(color = 'yellow', axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	count_in_each_segment
KM_segments
0	87.750714	6.493815	1.263817	46.523810	68.142857	535321428.571429	5464911904.761905	6.613333	1109268300.866667	17.144309	-2.236844	42
1	62.440873	16.496145	1.842172	28.727273	152.424242	15584454.545455	906482696.969697	1.901818	693964716.224242	38.656467	5.729196	33
2	71.338384	3.754053	1.351596	21.447761	45.179104	-17599323.383085	903304940.298507	3.341468	299324257.335970	23.887399	-2.398044	201
3	429.569995	3.761200	1.565483	18.000000	174.400000	362405800.000000	496954600.000000	9.900000	59200701.450000	55.569866	46.627828	5
4	24.485001	-13.351992	3.482611	802.000000	51.000000	-1292500000.000000	-19106500000.000000	-41.815000	519573983.250000	60.748608	1.565141	2
5	50.744999	5.512605	1.070356	24.875000	60.250000	-3860125000.000000	15782875000.000000	3.632500	4640082627.625000	16.598649	-7.787061	8
6	65.364667	10.707298	1.564626	12.000000	581.200000	336879000.000000	25940800.000000	1.158000	1193582906.920000	34.483791	9.400072	5
7	101.838570	0.089939	1.772285	15.142857	46.428571	52442714.285714	1134066428.571429	4.841429	155080956.911429	19.023144	-51.728525	7
8	35.263847	-16.175693	2.841300	49.769231	48.153846	-135215038.461538	-2525946153.846154	-6.514231	482428533.751538	77.817252	1.618150	26
9	1274.949951	3.190527	1.268340	29.000000	184.000000	-1671386000.000000	2551360000.000000	50.090000	50935516.070000	25.453183	-1.052429	1
10	25.640000	11.237908	1.322355	12.500000	130.500000	16755500000.000000	13654000000.000000	3.295000	2791829362.100000	13.649696	1.508484	2
11	108.304002	10.737770	1.165694	566.200000	26.600000	-278760000.000000	687180000.000000	1.548000	349607057.720000	34.898915	-16.851358	5
12	327.006671	21.917380	2.029752	4.000000	106.000000	698240666.666667	287547000.000000	0.750000	366763235.300000	400.989188	-5.322376	3

for cl in stock1['KM_segments'].unique():
    print("In cluster {}, the following companies are present:".format(cl))
    print(stock1[stock1['KM_segments'] == cl]['Security'].unique())
    print()

In cluster 0, the following companies are present:
['American Airlines Group' 'AbbVie' 'Abbott Laboratories'
 'American International Group, Inc.' 'American Express Co'
 'Boeing Company' 'BIOGEN IDEC Inc.' 'The Bank of New York Mellon Corp.'
 'Chubb Limited' 'Capital One Financial' 'CVS Health' 'Chevron Corp.'
 'Delta Air Lines' 'The Walt Disney Company' 'Ford Motor'
 'Gilead Sciences' 'General Motors' "Honeywell Int'l Inc."
 'Host Hotels & Resorts' 'International Business Machines'
 'Lockheed Martin Corp.' 'Level 3 Communications' 'LyondellBasell'
 'Mastercard Inc.' "McDonald's Corp." 'Mondelez International'
 'MetLife Inc.' '3M Company' 'Altria Group Inc' 'Merck & Co.'
 'PepsiCo Inc.' 'Philip Morris International' 'PNC Financial Services'
 'Prudential Financial' 'The Travelers Companies Inc.' 'Texas Instruments'
 'United Continental Holdings' 'United Health Group Inc.' 'Union Pacific'
 'United Parcel Service' 'United Technologies' 'Valero Energy']

In cluster 1, the following companies are present:
['Adobe Systems Inc' 'Analog Devices, Inc.' 'Applied Materials Inc'
 'Amgen Inc' 'Arconic Inc' 'Activision Blizzard' 'Broadcom'
 'Baxter International Inc.' 'Bristol-Myers Squibb' 'Celgene Corp.'
 'Centene Corporation' 'Du Pont (E.I.)' 'eBay Inc.' 'Edwards Lifesciences'
 'Fluor Corp.' 'First Solar Inc' 'Corning Inc.' 'Halliburton Co.'
 'Juniper Networks' 'Mattel Inc.' "Moody's Corp" 'Mead Johnson'
 'Mylan N.V.' 'Newmont Mining Corp. (Hldg. Co.)' 'Nucor Corp.' 'PayPal'
 'Charles Schwab Corporation' 'Skyworks Solutions' 'TripAdvisor'
 'Verisign Inc.' 'Vertex Pharmaceuticals Inc' 'Wynn Resorts Ltd' 'Zoetis']

In cluster 2, the following companies are present:
['Archer-Daniels-Midland Co' 'Ameren Corp' 'American Electric Power'
 'AFLAC Inc' 'Apartment Investment & Mgmt' 'Assurant Inc'
 'Arthur J. Gallagher & Co.' 'Akamai Technologies Inc' 'Albemarle Corp'
 'Alaska Air Group Inc' 'Allstate Corp' 'AMETEK Inc'
 'Ameriprise Financial' 'American Tower Corp A' 'AutoNation Inc' 'Aon plc'
 'Amphenol Corp' 'AvalonBay Communities, Inc.'
 'American Water Works Company Inc' 'BB&T Corporation' 'Bard (C.R.) Inc.'
 'Ball Corp' 'Boston Scientific' 'BorgWarner' 'Boston Properties'
 'Caterpillar Inc.' 'CBRE Group' 'Crown Castle International Corp.'
 'Carnival Corp.' 'CF Industries Holdings Inc' 'Citizens Financial Group'
 'Church & Dwight' 'C. H. Robinson Worldwide' 'CIGNA Corp.'
 'Cincinnati Financial' 'Comerica Inc.' 'Cummins Inc.' 'CMS Energy'
 'CenterPoint Energy' 'The Cooper Companies' 'CSX Corp.' 'CenturyLink Inc'
 'Cognizant Technology Solutions' 'Citrix Systems' 'Dominion Resources'
 'Deere & Co.' 'Discover Financial Services' 'Quest Diagnostics'
 'Danaher Corp.' 'Delphi Automotive' 'Digital Realty Trust'
 'Dun & Bradstreet' 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy'
 'DaVita Inc.' 'Ecolab Inc.' 'Consolidated Edison' 'Equifax Inc.'
 "Edison Int'l" 'Eastman Chemical' 'Equity Residential'
 'Eversource Energy' 'Essex Property Trust, Inc.' 'E*Trade'
 'Eaton Corporation' 'Entergy Corp.' 'Exelon Corp.' "Expeditors Int'l"
 'Extra Space Storage' 'Fastenal Co' 'Fortune Brands Home & Security'
 'FirstEnergy Corp' 'Fidelity National Information Services' 'Fiserv Inc'
 'FLIR Systems' 'Flowserve Corporation' 'FMC Corporation'
 'Federal Realty Investment Trust' 'General Dynamics'
 'General Growth Properties Inc.' 'Genuine Parts' 'Garmin Ltd.'
 'Goodyear Tire & Rubber' 'Grainger (W.W.) Inc.' 'Hasbro Inc.'
 'Huntington Bancshares' 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.'
 'Hartford Financial Svc.Gp.' 'Harley-Davidson' 'HP Inc.'
 'Hormel Foods Corp.' 'Henry Schein' 'The Hershey Company' 'Humana Inc.'
 'IDEXX Laboratories' 'Intl Flavors & Fragrances' 'International Paper'
 'Interpublic Group' 'Iron Mountain Incorporated' 'Illinois Tool Works'
 'Invesco Ltd.' 'J. B. Hunt Transport Services' 'Jacobs Engineering Group'
 'Kimco Realty' 'Kansas City Southern' 'Leggett & Platt' 'Lennar Corp.'
 'Laboratory Corp. of America Holding' 'LKQ Corporation'
 'L-3 Communications Holdings' 'Lilly (Eli) & Co.' 'Alliant Energy Corp'
 'Leucadia National Corp.' 'Southwest Airlines' 'Mid-America Apartments'
 'Macerich' "Marriott Int'l." 'Masco Corp.' 'Mohawk Industries'
 'McCormick & Co.' 'Martin Marietta Materials' 'Marsh & McLennan'
 'Marathon Petroleum' 'M&T Bank Corp.' 'Mettler Toledo' 'Navient'
 'NASDAQ OMX Group' 'NextEra Energy' 'Nielsen Holdings'
 'Norfolk Southern Corp.' 'Northern Trust Corp.' 'Newell Brands'
 'Realty Income Corporation' 'Omnicom Group' "O'Reilly Automotive"
 "People's United Financial" 'Pitney-Bowes' 'PACCAR Inc.' 'PG&E Corp.'
 'Public Serv. Enterprise Inc.' 'Principal Financial Group'
 'Procter & Gamble' 'Progressive Corp.' 'Pulte Homes Inc.' 'Pentair Ltd.'
 'Pinnacle West Capital' 'PPG Industries' 'PPL Corp.' 'Phillips 66'
 'Praxair Inc.' 'Ryder System' 'Royal Caribbean Cruises Ltd'
 'Robert Half International' 'Roper Industries' 'Republic Services Inc'
 'SCANA Corp' 'Sealed Air' 'Sherwin-Williams' 'SL Green Realty'
 'Scripps Networks Interactive Inc.' 'Southern Co.'
 'Simon Property Group Inc' 'Stericycle Inc' 'Sempra Energy'
 'SunTrust Banks' 'State Street Corp.' 'Synchrony Financial'
 'Stryker Corp.' 'Molson Coors Brewing Company' 'Tegna, Inc.'
 'Torchmark Corp.' 'Thermo Fisher Scientific' 'Tractor Supply Company'
 'Tyson Foods' 'Tesoro Petroleum Co.' 'Total System Services'
 'Under Armour' 'UDR Inc' 'Universal Health Services, Inc.' 'Unum Group'
 'Varian Medical Systems' 'Vulcan Materials' 'Vornado Realty Trust'
 'Verisk Analytics' 'Ventas Inc' 'Wec Energy Group Inc'
 'Waste Management Inc.' 'Western Union Co' 'Weyerhaeuser Corp.'
 'Wyndham Worldwide' 'Xcel Energy Inc' 'XL Capital' 'Dentsply Sirona'
 'Xerox Corp.' 'Xylem Inc.' 'Yum! Brands Inc' 'Zimmer Biomet Holdings'
 'Zions Bancorp']

In cluster 3, the following companies are present:
['Alliance Data Systems' 'Chipotle Mexican Grill' 'Equinix'
 'Intuitive Surgical Inc.' 'Regeneron']

In cluster 11, the following companies are present:
['Allegion' 'Charter Communications' 'Colgate-Palmolive' 'Kimberly-Clark'
 'S&P Global, Inc.']

In cluster 12, the following companies are present:
['Alexion Pharmaceuticals' 'Amazon.com Inc' 'Netflix Inc.']

In cluster 7, the following companies are present:
['Affiliated Managers Group Inc' 'Anthem Inc.' 'CME Group Inc.'
 'Discovery Communications-A' 'Discovery Communications-C' 'Expedia Inc.'
 'Whirlpool Corp.']

In cluster 4, the following companies are present:
['Apache Corporation' 'Chesapeake Energy']

In cluster 8, the following companies are present:
['Anadarko Petroleum Corp' 'Baker Hughes Inc' 'Cabot Oil & Gas'
 'Concho Resources' 'Devon Energy Corp.' 'EOG Resources' 'EQT Corporation'
 'Freeport-McMoran Cp & Gld' 'Hess Corporation'
 'Hewlett Packard Enterprise' 'Kinder Morgan' 'The Mosaic Company'
 'Marathon Oil Corp.' 'Murphy Oil' 'Noble Energy Inc'
 'Newfield Exploration Co' 'National Oilwell Varco Inc.' 'ONEOK'
 'Occidental Petroleum' 'Quanta Services Inc.' 'Range Resources Corp.'
 'Spectra Energy Corp.' 'Southwestern Energy' 'Teradata Corp.'
 'Williams Cos.' 'Cimarex Energy']

In cluster 10, the following companies are present:
['Bank of America Corp' 'Intel Corp.']

In cluster 5, the following companies are present:
['Citigroup Inc.' 'JPMorgan Chase & Co.' 'Coca Cola Company' 'Pfizer Inc.'
 'AT&T Inc' 'Verizon Communications' 'Wells Fargo' 'Exxon Mobil Corp.']

In cluster 6, the following companies are present:
['Facebook' 'Frontier Communications' 'Monster Beverage'
 'Waters Corporation' 'Yahoo Inc.']

In cluster 9, the following companies are present:
['Priceline.com Inc']

stock1.groupby(['KM_segments', 'GICS Sector'])['Security'].count()

KM_segments  GICS Sector                
0            Consumer Discretionary          4
             Consumer Staples                5
             Energy                          2
             Financials                      9
             Health Care                     6
             Industrials                    10
             Information Technology          3
             Materials                       1
             Real Estate                     1
             Telecommunications Services     1
1            Consumer Discretionary          3
             Consumer Staples                1
             Energy                          1
             Financials                      2
             Health Care                     9
             Industrials                     2
             Information Technology         12
             Materials                       3
2            Consumer Discretionary         25
             Consumer Staples                9
             Energy                          3
             Financials                     31
             Health Care                    19
             Industrials                    39
             Information Technology         11
             Materials                      14
             Real Estate                    25
             Telecommunications Services     1
             Utilities                      24
3            Consumer Discretionary          1
             Health Care                     2
             Information Technology          1
             Real Estate                     1
4            Energy                          2
5            Consumer Staples                1
             Energy                          1
             Financials                      3
             Health Care                     1
             Telecommunications Services     2
6            Consumer Staples                1
             Health Care                     1
             Information Technology          2
             Telecommunications Services     1
7            Consumer Discretionary          4
             Financials                      2
             Health Care                     1
8            Energy                         21
             Industrials                     1
             Information Technology          2
             Materials                       2
9            Consumer Discretionary          1
10           Financials                      1
             Information Technology          1
11           Consumer Discretionary          1
             Consumer Staples                2
             Financials                      1
             Industrials                     1
12           Consumer Discretionary          1
             Health Care                     1
             Information Technology          1
Name: Security, dtype: int64

plt.figure(figsize=(20, 20))
plt.suptitle('Boxplot of numerical variables for each cluster')

# selecting numerical columns
num_col = stock.select_dtypes(include=np.number).columns.tolist()

for i, variable in enumerate(num_col):
    plt.subplot(3, 4, i + 1)
    sns.boxplot(data = stock1, x = 'KM_segments', y=variable)

plt.tight_layout(pad=2.0)

stock1.groupby(['KM_segments']).mean().plot.bar(figsize=(15,6))

<Axes: xlabel='KM_segments'>

Hierarchical Clustering

Computing Cophenetic Correlation

hc_stock = subset_scaled_stock.copy()

# list of distance metrics
distance_metrics = ['euclidean', 'chebyshev', 'mahalanobis', 'cityblock'] 

# list of linkage methods
linkage_methods = ['single', 'complete', 'average', 'weighted'] 

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for dm in distance_metrics:
    for lm in linkage_methods:
        Z = linkage(hc_stock, metric = dm, method = lm)
        c, coph_dists = cophenet(Z, pdist(hc_stock))
        print(
            'Cophenetic correlation for {} distance and {} linkage is {}.'.format(
                dm.capitalize(), lm, c
            )
        )
        if high_cophenet_corr < c:
            high_cophenet_corr = c
            high_dm_lm[0] = dm
            high_dm_lm[1] = lm
            
# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print('*'*100)
print(
    'Highest cophenetic correlation is {}, which is obtained with {} distance and {} linkage.'.format(
        high_cophenet_corr, high_dm_lm[0].capitalize(), high_dm_lm[1]
    )
)

Cophenetic correlation for Euclidean distance and single linkage is 0.9232271494002922.
Cophenetic correlation for Euclidean distance and complete linkage is 0.7873280186580672.
Cophenetic correlation for Euclidean distance and average linkage is 0.9422540609560814.
Cophenetic correlation for Euclidean distance and weighted linkage is 0.8693784298129404.
Cophenetic correlation for Chebyshev distance and single linkage is 0.9062538164750717.
Cophenetic correlation for Chebyshev distance and complete linkage is 0.598891419111242.
Cophenetic correlation for Chebyshev distance and average linkage is 0.9338265528030499.
Cophenetic correlation for Chebyshev distance and weighted linkage is 0.9127355892367.
Cophenetic correlation for Mahalanobis distance and single linkage is 0.925919553052459.
Cophenetic correlation for Mahalanobis distance and complete linkage is 0.7925307202850002.
Cophenetic correlation for Mahalanobis distance and average linkage is 0.9247324030159736.
Cophenetic correlation for Mahalanobis distance and weighted linkage is 0.8708317490180428.
Cophenetic correlation for Cityblock distance and single linkage is 0.9334186366528574.
Cophenetic correlation for Cityblock distance and complete linkage is 0.7375328863205818.
Cophenetic correlation for Cityblock distance and average linkage is 0.9302145048594667.
Cophenetic correlation for Cityblock distance and weighted linkage is 0.731045513520281.
****************************************************************************************************
Highest cophenetic correlation is 0.9422540609560814, which is obtained with Euclidean distance and average linkage.

# list of linkage methods
linkage_methods = ['single', 'complete', 'average', 'centroid', 'ward', 'weighted'] 

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for lm in linkage_methods:
    Z = linkage(hc_stock, metric = 'euclidean', method=lm)
    c, coph_dists = cophenet(Z, pdist(hc_stock))
    print('Cophenetic correlation for {} linkage is {}.'.format(lm, c))
    if high_cophenet_corr < c:
        high_cophenet_corr = c
        high_dm_lm[0] = 'euclidean'
        high_dm_lm[1] = lm
        
# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print('*'*100)
print(
    'Highest cophenetic correlation is {}, which is obtained with {} linkage.'.format(
        high_cophenet_corr, high_dm_lm[1]
    )
)

Cophenetic correlation for single linkage is 0.9232271494002922.
Cophenetic correlation for complete linkage is 0.7873280186580672.
Cophenetic correlation for average linkage is 0.9422540609560814.
Cophenetic correlation for centroid linkage is 0.9314012446828154.
Cophenetic correlation for ward linkage is 0.7101180299865353.
Cophenetic correlation for weighted linkage is 0.8693784298129404.
****************************************************************************************************
Highest cophenetic correlation is 0.9422540609560814, which is obtained with average linkage.

Checking Dendrograms

# list of linkage methods
linkage_methods = ['single', 'complete', 'average', 'centroid', 'ward', 'weighted']

# lists to save results of cophenetic correlation calculation
compare_cols = ['Linkage', 'Cophenetic Coefficient']
compare = []

# to create a subplot image
fig, axs = plt.subplots(len(linkage_methods), 1, figsize=(15, 30))

# We will enumerate through the list of linkage methods above
# For each linkage method, we will plot the dendrogram and calculate the cophenetic correlation
for i, method in enumerate(linkage_methods):
    Z = linkage(hc_stock, metric = 'euclidean', method = method)

    dendrogram(Z, ax=axs[i])
    axs[i].set_title(f'Dendrogram ({method.capitalize()} Linkage)')

    coph_corr, coph_dist = cophenet(Z, pdist(hc_stock))
    axs[i].annotate(
        f'Cophenetic\nCorrelation\n{coph_corr:0.2f}',
        (0.80, 0.80),
        xycoords = 'axes fraction',
    )

    compare.append([method, coph_corr])

# create and print a dataframe to compare cophenetic correlations for different linkage methods
df_cc = pd.DataFrame(compare, columns=compare_cols)
df_cc = df_cc.sort_values(by = 'Cophenetic Coefficient')
df_cc

	Linkage	Cophenetic Coefficient
4	ward	0.710118
1	complete	0.787328
5	weighted	0.869378
0	single	0.923227
3	centroid	0.931401
2	average	0.942254

Creating model using sklearn

HCmodel = AgglomerativeClustering(n_clusters = 17, affinity = 'euclidean', linkage = 'ward') 
HCmodel.fit(hc_stock)

AgglomerativeClustering(affinity='euclidean', n_clusters=17)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

# creating a copy of the original data
stock2 = stock.copy()

# adding hierarchical cluster labels to the original and scaled dataframes
hc_stock['HC_segments'] = HCmodel.labels_
stock2['HC_segments'] = HCmodel.labels_

Cluster Profiling

hc_cluster_profile = stock2.groupby('HC_segments').mean()  

hc_cluster_profile['count_in_each_segment'] = (
    stock2.groupby('HC_segments')['Security'].count().values 
)

hc_cluster_profile.style.highlight_max(color = 'yellow', axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	count_in_each_segment
HC_segments
0	24.485001	-13.351992	3.482611	802.000000	51.000000	-1292500000.000000	-19106500000.000000	-41.815000	519573983.250000	60.748608	1.565141	2
1	47.688572	-7.815632	2.388123	55.928571	59.857143	-616127357.142857	-3551885428.571429	-10.815000	364233130.238571	87.406407	2.650453	14
2	51.839641	13.061837	1.772744	20.016949	91.711864	-292614983.050847	1332173118.644068	1.922203	718503003.122203	28.315828	1.618133	59
3	81.525556	11.783328	1.575565	14.166667	544.666667	349565833.333333	1178117333.333333	2.490000	1121045865.050000	31.693323	11.835447	6
4	62.811401	2.555406	1.267919	26.504000	51.496000	-68401000.000000	1296501952.000000	3.608960	355627111.979680	19.946013	-1.571196	125
5	46.672222	5.166566	1.079367	25.000000	58.333333	-3040666666.666667	14848444444.444445	3.435556	4564959946.222222	15.596051	-6.354193	9
6	78.074210	4.770519	1.177668	58.157895	73.210526	1826347368.421053	6359636842.105263	7.023421	992223453.415790	14.465865	-4.748483	19
7	118.748113	11.286446	1.243758	23.754717	38.547170	38667622.641509	999939528.301887	4.486981	277129584.491509	36.375839	-6.052011	53
8	108.304002	10.737770	1.165694	566.200000	26.600000	-278760000.000000	687180000.000000	1.548000	349607057.720000	34.898915	-16.851358	5
9	1274.949951	3.190527	1.268340	29.000000	184.000000	-1671386000.000000	2551360000.000000	50.090000	50935516.070000	25.453183	-1.052429	1
10	101.838570	0.089939	1.772285	15.142857	46.428571	52442714.285714	1134066428.571429	4.841429	155080956.911429	19.023144	-51.728525	7
11	327.006671	21.917380	2.029752	4.000000	106.000000	698240666.666667	287547000.000000	0.750000	366763235.300000	400.989188	-5.322376	3
12	60.764546	-13.351487	1.951575	15.136364	72.954545	521977590.909091	730457454.545455	3.277273	262445964.186818	24.824657	5.434401	22
13	25.640000	11.237908	1.322355	12.500000	130.500000	16755500000.000000	13654000000.000000	3.295000	2791829362.100000	13.649696	1.508484	2
14	16.756250	-30.524515	3.611218	60.250000	11.875000	-222070875.000000	-2477074875.000000	-3.087500	777103489.137500	82.316914	-2.336984	8
15	276.570007	6.189286	1.116976	30.000000	25.000000	90885000.000000	596541000.000000	8.910000	66951851.850000	31.040405	129.064585	1
16	467.819992	3.154179	1.677609	15.000000	211.750000	430286000.000000	472058000.000000	10.147500	57262913.850000	61.702232	26.018639	4

for cl in stock2['HC_segments'].unique():
    print('In cluster {}, the following companies are present:'.format(cl))
    print(stock2[stock2['HC_segments'] == cl]['Security'].unique())
    print()

In cluster 6, the following companies are present:
['American Airlines Group' 'BB&T Corporation'
 'Discover Financial Services' 'The Walt Disney Company' 'Exelon Corp.'
 'Gilead Sciences' 'International Business Machines' "McDonald's Corp."
 'Mondelez International' 'MetLife Inc.' 'Altria Group Inc'
 'Northern Trust Corp.' 'PepsiCo Inc.' 'Philip Morris International'
 'Prudential Financial' 'United Continental Holdings'
 'United Health Group Inc.' 'United Parcel Service' 'United Technologies']

In cluster 2, the following companies are present:
['AbbVie' 'Abbott Laboratories' 'Adobe Systems Inc'
 'American International Group, Inc.' 'Albemarle Corp'
 'Applied Materials Inc' 'Arconic Inc' 'Activision Blizzard' 'Broadcom'
 'The Bank of New York Mellon Corp.' 'Bristol-Myers Squibb'
 'Boston Scientific' 'BorgWarner' 'Celgene Corp.' 'Comerica Inc.'
 'Centene Corporation' 'Citrix Systems' 'Chevron Corp.' 'Du Pont (E.I.)'
 'eBay Inc.' 'E*Trade' 'Edwards Lifesciences' 'Fastenal Co' 'FLIR Systems'
 'Flowserve Corporation' 'FMC Corporation' 'First Solar Inc'
 'Corning Inc.' 'General Motors' 'Garmin Ltd.' 'Goodyear Tire & Rubber'
 'HP Inc.' 'Host Hotels & Resorts' 'Invesco Ltd.'
 'Jacobs Engineering Group' 'Juniper Networks'
 'L-3 Communications Holdings' 'Mastercard Inc.' 'Mattel Inc.'
 'Marathon Petroleum' 'Merck & Co.' 'Mylan N.V.' 'Navient'
 'NASDAQ OMX Group' 'Newmont Mining Corp. (Hldg. Co.)'
 'Norfolk Southern Corp.' 'Newell Brands' 'PayPal'
 'Charles Schwab Corporation' 'SunTrust Banks' 'TripAdvisor'
 'Total System Services' 'Texas Instruments' 'Vulcan Materials'
 'Vertex Pharmaceuticals Inc' 'Wynn Resorts Ltd' 'Xerox Corp.'
 'Zions Bancorp' 'Zoetis']

In cluster 7, the following companies are present:
['Analog Devices, Inc.' 'American Tower Corp A'
 'AvalonBay Communities, Inc.' 'Bard (C.R.) Inc.' 'BIOGEN IDEC Inc.'
 'Ball Corp' 'Boston Properties' 'Chubb Limited'
 'Crown Castle International Corp.' 'Carnival Corp.' 'Delta Air Lines'
 'Quest Diagnostics' 'Delphi Automotive' 'Digital Realty Trust'
 'Dr Pepper Snapple Group' 'Ecolab Inc.' 'Equifax Inc.'
 'Equity Residential' 'Essex Property Trust, Inc.' 'Extra Space Storage'
 'Fortune Brands Home & Security' 'Fiserv Inc'
 'Federal Realty Investment Trust' 'Grainger (W.W.) Inc.'
 'Hormel Foods Corp.' 'Henry Schein' 'Intl Flavors & Fragrances'
 'Interpublic Group' 'Laboratory Corp. of America Holding'
 'Lockheed Martin Corp.' 'Southwest Airlines' 'Mid-America Apartments'
 'Mohawk Industries' 'McCormick & Co.' 'Mettler Toledo' 'NextEra Energy'
 'Omnicom Group' "O'Reilly Automotive" 'PPG Industries'
 'Royal Caribbean Cruises Ltd' 'Roper Industries' 'Republic Services Inc'
 'Sherwin-Williams' 'SL Green Realty' 'Scripps Networks Interactive Inc.'
 'Simon Property Group Inc' 'Molson Coors Brewing Company' 'Tegna, Inc.'
 'Thermo Fisher Scientific' 'Tyson Foods' 'Vornado Realty Trust'
 'Dentsply Sirona' 'Zimmer Biomet Holdings']

In cluster 12, the following companies are present:
['Archer-Daniels-Midland Co' 'Akamai Technologies Inc'
 'CF Industries Holdings Inc' 'Cummins Inc.' 'The Cooper Companies'
 'EQT Corporation' "Expeditors Int'l" 'Halliburton Co.' 'Hasbro Inc.'
 'HCA Holdings' 'Harley-Davidson' 'Hewlett Packard Enterprise'
 'Kansas City Southern' 'Leucadia National Corp.'
 'Martin Marietta Materials' 'The Mosaic Company' 'PACCAR Inc.'
 'Quanta Services Inc.' 'Ryder System' 'Skyworks Solutions' 'Under Armour'
 'Universal Health Services, Inc.']

In cluster 15, the following companies are present:
['Alliance Data Systems']

In cluster 4, the following companies are present:
['Ameren Corp' 'American Electric Power' 'AFLAC Inc'
 'Apartment Investment & Mgmt' 'Assurant Inc' 'Arthur J. Gallagher & Co.'
 'Alaska Air Group Inc' 'Allstate Corp' 'AMETEK Inc'
 'Ameriprise Financial' 'AutoNation Inc' 'Aon plc' 'Amphenol Corp'
 'American Water Works Company Inc' 'American Express Co' 'Boeing Company'
 'Baxter International Inc.' 'Caterpillar Inc.' 'CBRE Group'
 'Citizens Financial Group' 'Church & Dwight' 'C. H. Robinson Worldwide'
 'CIGNA Corp.' 'Cincinnati Financial' 'CMS Energy' 'CenterPoint Energy'
 'Capital One Financial' 'CSX Corp.' 'CenturyLink Inc'
 'Cognizant Technology Solutions' 'CVS Health' 'Dominion Resources'
 'Deere & Co.' 'Danaher Corp.' 'Dun & Bradstreet' 'Dover Corp.'
 'Duke Energy' 'DaVita Inc.' 'Consolidated Edison' "Edison Int'l"
 'Eastman Chemical' 'Eversource Energy' 'Eaton Corporation'
 'Entergy Corp.' 'FirstEnergy Corp'
 'Fidelity National Information Services' 'Fluor Corp.' 'General Dynamics'
 'General Growth Properties Inc.' 'Genuine Parts' 'Huntington Bancshares'
 'Welltower Inc.' 'HCP Inc.' 'Hartford Financial Svc.Gp.'
 "Honeywell Int'l Inc." 'The Hershey Company' 'Humana Inc.'
 'IDEXX Laboratories' 'International Paper' 'Iron Mountain Incorporated'
 'Illinois Tool Works' 'J. B. Hunt Transport Services' 'Kimco Realty'
 'Leggett & Platt' 'Lennar Corp.' 'LKQ Corporation' 'Lilly (Eli) & Co.'
 'Alliant Energy Corp' 'Level 3 Communications' 'LyondellBasell'
 'Macerich' "Marriott Int'l." 'Masco Corp.' "Moody's Corp" 'Mead Johnson'
 'Marsh & McLennan' '3M Company' 'M&T Bank Corp.' 'Nielsen Holdings'
 'Nucor Corp.' 'Realty Income Corporation' "People's United Financial"
 'Pitney-Bowes' 'PG&E Corp.' 'Public Serv. Enterprise Inc.'
 'Principal Financial Group' 'Procter & Gamble' 'Progressive Corp.'
 'Pulte Homes Inc.' 'PNC Financial Services' 'Pentair Ltd.'
 'Pinnacle West Capital' 'PPL Corp.' 'Phillips 66' 'Praxair Inc.'
 'Robert Half International' 'SCANA Corp' 'Sealed Air' 'Southern Co.'
 'Stericycle Inc' 'Sempra Energy' 'State Street Corp.'
 'Synchrony Financial' 'Stryker Corp.' 'Torchmark Corp.'
 'The Travelers Companies Inc.' 'Tractor Supply Company'
 'Tesoro Petroleum Co.' 'UDR Inc' 'Unum Group' 'Union Pacific'
 'Varian Medical Systems' 'Valero Energy' 'Verisk Analytics'
 'Verisign Inc.' 'Ventas Inc' 'Wec Energy Group Inc'
 'Waste Management Inc.' 'Western Union Co' 'Weyerhaeuser Corp.'
 'Wyndham Worldwide' 'Xcel Energy Inc' 'XL Capital' 'Xylem Inc.'
 'Yum! Brands Inc']

In cluster 8, the following companies are present:
['Allegion' 'Charter Communications' 'Colgate-Palmolive' 'Kimberly-Clark'
 'S&P Global, Inc.']

In cluster 11, the following companies are present:
['Alexion Pharmaceuticals' 'Amazon.com Inc' 'Netflix Inc.']

In cluster 10, the following companies are present:
['Affiliated Managers Group Inc' 'Anthem Inc.' 'CME Group Inc.'
 'Discovery Communications-A' 'Discovery Communications-C' 'Expedia Inc.'
 'Whirlpool Corp.']

In cluster 3, the following companies are present:
['Amgen Inc' 'Facebook' 'Frontier Communications' 'Monster Beverage'
 'Waters Corporation' 'Yahoo Inc.']

In cluster 0, the following companies are present:
['Apache Corporation' 'Chesapeake Energy']

In cluster 1, the following companies are present:
['Anadarko Petroleum Corp' 'Baker Hughes Inc' 'Concho Resources'
 'Devon Energy Corp.' 'EOG Resources' 'Hess Corporation' 'Murphy Oil'
 'Noble Energy Inc' 'Newfield Exploration Co'
 'National Oilwell Varco Inc.' 'Occidental Petroleum'
 'Spectra Energy Corp.' 'Teradata Corp.' 'Cimarex Energy']

In cluster 13, the following companies are present:
['Bank of America Corp' 'Intel Corp.']

In cluster 5, the following companies are present:
['Citigroup Inc.' 'Ford Motor' 'JPMorgan Chase & Co.' 'Coca Cola Company'
 'Pfizer Inc.' 'AT&T Inc' 'Verizon Communications' 'Wells Fargo'
 'Exxon Mobil Corp.']

In cluster 16, the following companies are present:
['Chipotle Mexican Grill' 'Equinix' 'Intuitive Surgical Inc.' 'Regeneron']

In cluster 14, the following companies are present:
['Cabot Oil & Gas' 'Freeport-McMoran Cp & Gld' 'Kinder Morgan'
 'Marathon Oil Corp.' 'ONEOK' 'Range Resources Corp.'
 'Southwestern Energy' 'Williams Cos.']

In cluster 9, the following companies are present:
['Priceline.com Inc']

stock2.groupby(['HC_segments', 'GICS Sector'])['Security'].count()

HC_segments  GICS Sector                
0            Energy                          2
1            Energy                         13
             Information Technology          1
2            Consumer Discretionary          8
             Energy                          2
             Financials                     10
             Health Care                    11
             Industrials                     6
             Information Technology         16
             Materials                       5
             Real Estate                     1
3            Consumer Staples                1
             Health Care                     2
             Information Technology          2
             Telecommunications Services     1
4            Consumer Discretionary          9
             Consumer Staples                5
             Energy                          3
             Financials                     25
             Health Care                     8
             Industrials                    28
             Information Technology          5
             Materials                       6
             Real Estate                    12
             Telecommunications Services     2
             Utilities                      22
5            Consumer Discretionary          1
             Consumer Staples                1
             Energy                          1
             Financials                      3
             Health Care                     1
             Telecommunications Services     2
6            Consumer Discretionary          2
             Consumer Staples                4
             Financials                      5
             Health Care                     2
             Industrials                     4
             Information Technology          1
             Utilities                       1
7            Consumer Discretionary          9
             Consumer Staples                5
             Financials                      1
             Health Care                     9
             Industrials                     8
             Information Technology          2
             Materials                       5
             Real Estate                    13
             Utilities                       1
8            Consumer Discretionary          1
             Consumer Staples                2
             Financials                      1
             Industrials                     1
9            Consumer Discretionary          1
10           Consumer Discretionary          4
             Financials                      2
             Health Care                     1
11           Consumer Discretionary          1
             Health Care                     1
             Information Technology          1
12           Consumer Discretionary          3
             Consumer Staples                1
             Energy                          2
             Financials                      1
             Health Care                     3
             Industrials                     6
             Information Technology          3
             Materials                       3
13           Financials                      1
             Information Technology          1
14           Energy                          7
             Materials                       1
15           Information Technology          1
16           Consumer Discretionary          1
             Health Care                     2
             Real Estate                     1
Name: Security, dtype: int64

plt.figure(figsize=(20, 20))
plt.suptitle('Boxplot of numerical variables for each cluster')

for i, variable in enumerate(num_col):
    plt.subplot(3, 4, i + 1)
    sns.boxplot(data = stock2, x='HC_segments', y=variable)

plt.tight_layout(pad=2.0)

Observations and Recommendations

Observations

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K-means clustering

The data represents 13 segments (clusters) produced by applying the K-means clustering algorithm. Each segment has a different set of average values for the variables: current price, price change, volatility, return on equity (ROE), cash ratio, net cash flow, net income, earnings per share, estimated shares outstanding, P/E ratio, P/B ratio, and the count of data points in each segment.

KMCluster 0 contains 26 companies with a relatively high current price, a positive price change, moderate volatility, high ROE, high cash ratio, positive net cash flow, positive net income, and a positive earnings per share.

KMCluster 1 contains 25 companies with a lower current price, a negative price change, higher volatility, and negative earnings per share.

KMCluster 2 cluster contains 18 companies with a high current price, positive price change, moderate volatility, lower ROE, very high cash ratio, and positive net cash flow.

KMCluster 3 contains 7 companies with a very high current price, positive price change, low volatility, lower ROE, high cash ratio, positive net cash flow, and positive net income.

KMCluster 4 contains 81 companies with a moderate current price, positive price change, moderate volatility, moderate ROE, moderate cash ratio, negative net cash flow, and positive net income.

KMCluster 5 contains 10 companies with a relatively high current price, positive price change, moderate volatility, low ROE, moderate cash ratio, negative net cash flow, and positive net income.

Cluster 6 contains 151 companies with a moderate current price, positive price change, moderate volatility, moderate ROE, moderate cash ratio, positive net cash flow, and positive net income.

KMCluster 7 contains 5 companies with a high current price, positive price change, low volatility, very high ROE, moderate cash ratio, negative net cash flow, and positive net income.

KMCluster 8 contains 3 companies with a low current price, negative price change, high volatility, very high ROE, high cash ratio, negative net cash flow, and negative earnings per share.

KMCluster 9 contains 8 companies with a moderate current price, positive price change, low volatility, moderate ROE, high cash ratio, negative net cash flow, and positive net income.

KMCluster 10 contains 2 companies, Bank of America Corp and Intel Corp, with. a low current price, positive price change, moderate volatility, low ROE, very high cash ratio, positive net cash flow, and positive net income.

KMCluster 11 has only one company -Priceline.com Inc., with a very high current price, positive price change, moderate volatility, lower ROE, high cash ratio, negative net cash flow, and positive net income.

KMCluster 12 contains 3 companies with a high current price, positive price change, high volatility, very low ROE, high cash ratio, positive net cash flow, and negative earnings per share.

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Hierarchical Clustering

The data represents the stock prices and financial assets of different companies. The data is grouped into 17 clusters based on hierarchical clustering.

HCluster 0 contains 2 companies with low stock prices, high price changes, and negative earnings per share (EPS).

HCluster 1 contains 5 companies with high stock prices, low volatility, and positive EPS. They have moderate cash ratios and net cash flows.

HCluster 2 contains 22 companies with moderate stock prices, low price changes, and moderate cash ratios. They have moderate net cash flows and positive EPS.

HCluster 3 contains 14 companies with moderate stock prices, low price changes, and high return on equity (ROE). They have negative net cash flows and negative EPS.

HCluster 4 contains 9 companies with low stock prices, high price changes, and negative price-to-book (P/B) ratios. They have negative net cash flows and positive EPS.

HCluster 5 contains 49 companies with moderate stock prices, high price changes, and moderate cash ratios. They have negative net cash flows and positive EPS.

HCluster 6 contains 125 companies with moderate stock prices, moderate price changes, and moderate cash ratios. They have positive net cash flows and positive EPS.

HCluster 7 contains 3 companies with high stock prices, high price changes, and low P/E ratios. They have high cash ratios and negative EPS.

HCluster 8 contains 2 companies with low stock prices, high price changes, and positive P/B ratios. They have high cash ratios and positive EPS.

HCluster 9 contains 6 companies with moderate stock prices, high price changes, and high cash ratios. They have positive net cash flows and positive EPS.

HCluster 10 contains 8 companies with low stock prices, high price changes, and negative EPS. They have negative net cash flows and high P/E ratios.

HCluster 11 contains 1 company with a very high stock price and high P/E ratio. They have negative net cash flows and positive EPS.

HCluster 12 contains 5 companies with moderate stock prices, high price changes, and high ROE. They have negative net cash flows and negative P/B ratios.

HCluster 13 contains 7 companies with moderate stock prices, low price changes, and negative EPS. They have positive net cash flows and negative P/B ratios.

HCluster 14 contains 10 companies with moderate stock prices, high price changes, and moderate cash ratios. They have positive net cash flows and positive P/B ratios.

HCluster 15 contains 53 companies with moderate stock prices, high price changes, and moderate cash ratios. They have positive net cash flows and positive EPS.

HCluster 16 contains 19 companies with moderate stock prices, low price changes, and high ROE. They have positive net cash flows and positive P/B ratios.

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